Goldbach Conjecture and Prime Number Constraints

In a letter written to Euler in 1742 Christian Goldbach conjectured that every even number is the sum of two prime numbers. This animation depicts the different sets of (sets of prime/composite numbers) with cardinality=x that could satisfy this constriant. Of these sets, the true set of prime numbers is included if the Goldbach Conjecture is true. This set, represented as the bits of the integer on the Ulam Spiral, is displayed in the appropiate place. The spiral only contains odd numbers. A white line indicates the path taken as the true prime number set is resolved bit by bit. The entire spiral is initially colored with the spectrum according to the number of primes (bits that are on) in the set. Those sets with few primes are colored red, and those with many are blue and violet. As the number of bits increase some sets are rulled out because they would not conform to the Goldbach Conjecture. These sets are turned to black. The true set of prime numbers, assuming GC, is constrained to lie on the colored regions of the animation as it grows in lockstep with π(x).

Category:

Science & Technology

Tags:

• Goldbach
• Conjecture
• Ulam
• Spiral
• Prime
• Numbers
• math
• mathematics
• paske

[spaske2528]

This video shows the sets of bitstrings which when reversed and AND'ed with themselves lead to a result>0 for bitstrings with length N as N increases. If the Goldbach conjecture is correct, then the set of primes represented as a bit-string must be one of the colored pixels in the animation, but the animation does not make any other claims.

[Werelion2367]

if the conjecture is true, does it say that every prime number is used, or even that everyone can bwe used just once?